Valjeane C. King, a mother of five who stole more than $40,000 in welfare payments while employed at the D.C. Human Resources Department, was sentenced yesterday to six months in jail.

U.S. District Judge John J. Sirica said he was imposing the jail term to deter others from committing similar crimes. "It is a warning to somebody sitting in an office that they aren't going to get a slap on the wrist" when they are convicted of white-collar crimes, Sirica said at sentencing.

Mrs. King's scheme to earn illegal welfare payments over a four-year period won her the title of "Queen of Welfare Fraud" from federal prosecutors here, a nickname both she and her attorney disputed at her sentencing.

"I did it because I loved my children," Mrs. King said. "I seen my family falling apart and I tried to do something to hold it together."

Her attorney, Mark W. Foster, said there was no evidence that Mrs. King had spent the money on "any sort of wild living . . . no fancy clothes, no parties, no liquor.

"The facts are plain. She spent the money she stole on providing a decent place for herself and her children to live," Foster said. Mrs. King, whose children range from 7 to 17, is 33.

Assistant U.S. Attorney Richard Beizer of the fraud division had asked for a substantial sentence because he said she was a public official who betrayed the public trust.

The Human Resources Department "became for the defendant a unique type of lending agency - one that required no interest and no payback of principal," Beizer said. Mrs. King was a $10,000-a-year clerk with the Human Resources Department when her welfare fraud scheme was uncovered.

She admitted guilt to one count of false pretenses, and could have received a maximum sentence of 1-to-3 years. According to Beizer, she falsified documents to have checks sent to her in her name and in the name of "Marie Simpson," and then cashed those checks.

Mrs. King's voice choked with tears as she pleaded with Sirica for mercy. "I'm truly and deeply sorry for the wrong I've done and for the harm that it's done to my family," she said.

Sirica said he was impressed with what he felt was a true expression of remorse on her part, but that he felt the deterrence of a jail sentence was necessary in her case.

She is third person prosecuted in federal court here in the last six months for receiving illegal welfare payments as part of a continuing investigation of welfare cheats here.

The other two defendants also received prison sentences, and investigators have said the imposition of the jail terms has resulted in scores of persons making voluntary changes in their welfare status to correct past improper filings.

A recent General Accounting Office report estimated that the District of Columbia paid out an estimated $8.7 million in welfare funds to illegal recipients in 1975.

It was the latest in a series of recent studies revealing that millions of dollars have been wasted annually through managment deficiencies in programs to aid the poor that are run by the Human Resources Department.

DHR officials have attributed the losses to staff problems and various complex changes in welfare laws, and have said they have taken detailed steps to correct any problems. DHR investigators conducted the probe that resulted in Mrs. King's guilty plea and sentence.